Orthogonal frequency-division multiplexing (OFDM) is a method of digital modulation in which a signal is split into several narrowband channels at different frequencies. In some respects, OFDM is similar to conventional frequency-division multiplexing (FDM). The difference lies in the way in which the signals are modulated and demodulated. In general, priority is given to minimizing the interference, or crosstalk, among the channels and symbols comprising the data stream, while less importance is placed on perfecting individual channels.
OFDM-based communication is used in a wide variety of applications, including in European digital audio broadcast services, digital television, wireless local area networks, and is being considered as a method of obtaining high-speed digital data transmission over conventional telephone lines. OFDM systems have been widely used in high speed digital communication systems, such as VHDSL and ADSL since OFDM systems convert intersymbol interference (ISI) channels into ISI-free channels by inserting a cyclic prefix (CP) as an overhead of the data rate at the transmitter. Thus, OFDM is a widely-used technique for wireless and other types of communications.
In OFDM, data is transmitted in parallel over multiple equally spaced carrier frequencies using Fourier transform methods for modulation and demodulation. By inserting a guard period or guard interval, referred to as a cyclic prefix (CP), between symbols, data on OFDM subcarriers can be received orthogonally with no inter-carrier interference (ICI) and no intersymbol interference (ISI). Eliminating the ICI and ISI mitigates the effects of delay spread, making OFDM well-suited to wireless multipath channels. Moreover, for wireless channels, OFDM can be used with coding to easily exploit frequency diversity and combat Rayleigh fading to improve reliable information transfer.
OFDM-based systems, including orthogonal frequency division multiple access (OFDMA) systems, divide an available bandwidth into a plurality of orthogonal frequency subcarriers. Various subsets of the subcarriers may be assigned for use in communications, such as communications between particular stations. The particular subcarriers and the number of subcarriers assigned for use with respect to a communication may be based upon such considerations as the bandwidth or throughput to be provided by the radio link, interference mitigation or avoidance, etcetera. In an OFDMA system, multiple stations (e.g., subscriber stations) may be simultaneously provided communication links with a common access point (e.g., base station) or other station by simultaneously assigning different subsets of the subcarriers for the links of the multiple stations.
In OFDM and OFDMA communications, a signal is split into a number of sub-signals which are then transmitted simultaneously on different ones of the subcarriers. These separate subsignals may then be recombined by a receiving station to form the original signal for further processing etcetera.
Communication access is typically provided to the various stations through a defined protocol, such as may require access, resource allocation, authorization, and registration. It is common to use a ranging process as part of an access protocol in OFDM and OFDMA systems. In a typical ranging process, a subscriber station desiring access to network resources transmits a ranging code on a pre-specified set of subcarriers. That is, the subscriber station transmits a ranging code spread over multiple subcarriers which form the ranging subchannel. The ranging code may be a random or quasi-random code (e.g., code division multiple access (CDMA) chip code). The base station extracts the ranging code from the received signal and estimates the corresponding time delay. The time delay is used by the base station for transmission time delay estimation used with respect to downlink and uplink resources assigned to the subscriber station for further communications.
OFDM-based communication is well known in the art. A brief discussion thereof is provided herein, but the description of OFDM provided herein is not intended to limit the scope or applicability of the present invention in any way. An OFDM symbol has 2M+1 complex sinusoids modulated by complex modulation values {X(j)}, where j is the subcarrier index. The output OFDM symbol of length N samples, with time index k, is given by the N-point complex modulation sequence:
            x      ⁡              (        k        )              =                  1        N            ⁢                        ∑                      j            =                          -              M                                M                ⁢                              X            ⁡                          (              j              )                                ⁢                      ⅇ                          j              ⁢                                                          ⁢              2              ⁢                                                          ⁢              π              ⁢                                                          ⁢                              kj                /                N                                                          ,k=0, 1, 2, . . . , N−1; N≧2M+1. This process is efficiently carried out using an inverse DFT. The individual sinusoids are orthogonal on the useful interval of the symbol. For a sample interval of Ts, the separation of subcarriers is 1/N·Ts), and the useful period of the symbol is Tu=N·Ts.
To mitigate against intersymbol interference (ISI), a cyclic prefix (CP), or guard interval, of Ng samples, is inserted before each symbol. The guard interval of Tg=Ng·Ts is generally chosen to exceed the largest expected multipath delay. The periodic nature of the DFT is exploited by making the guard interval a replica of the last Ng symbols of the symbol. The transmitted symbol thus has Ns=N+Ng samples.
In the multipath channel case, assume there are P+1 paths indexed as [0, 1, . . . , P]. The path amplitude of the p-th path is denoted as αp, and the path delay of the p-th path is denoted as θp. The system frequency offset is denoted as ε. The received signal r(k) can be written as: r(k)=Σαps(k−θp)ej2πε(k−θp)/N+n(k), where s(k) is the transmitted signal, n(k) is the additive white noise.
OFDM has superb robustness to ISI as a consequence of employing the CP. For adequate performance, an ISI free symbol is desired for presentation to the FFT process, and thus timing estimation becomes an important consideration in OFDM-based communication. Thus, it is well-known that OFDM-based systems demand strict timing and frequency synchronization between the transmitter and receiver. To avoid ISI, the receiver should adjust its symbol timing so that the symbol transitions occur within the cyclic prefixes between the symbols. In a multipath channel, the CP contains the symbol transitions under all signal paths. Also, being a multicarrier system, the OFDM receiver and transmitter should be tightly frequency synchronized in order to avoid ICI.
Several methods have been proposed for OFDM time and frequency synchronization. A number of timing synchronization algorithms have been proposed in the art, many of which exploit the correlation properties of the CP. As examples, various timing synchronization algorithms are proposed in the following references, the disclosures of which are hereby incorporated herein by reference:    1) J.-J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Transactions, on Signal Processing, vol. 45, no. 7, pp. 1800-1805, 1997;    2) C. Williams, M. A. Beach, and S. McLaughlin, “Robust OFDM timing synchronisation,” Electronics Letters, vol. 41, no. 13, pp. 751-752, 2005;    3) T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Transactions on Communications, vol. 45, no. 12, pp. 1613-1621, 1997;    4) D. Landstrom, S. K. Wilson, J.-J. van de Beek, P. Odling, and P. O. Borjesson, “Symbol time offset estimation in coherent OFDM systems,” IEEE Transactions on Communications, vol. 50, no. 4, pp. 545-549, 2002;    5) H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequency synchronization for OFDM systems,” IEEE Transactions on Wireless Communications, vol. 2, no. 4, pp. 822-839, 2003;    6) M.-H. Hsieh and C.-H. Wei, “A low-complexity frame synchronization and frequency offset compensation scheme for OFDM systems over fading channels,” IEEE Transactions on Vehicular Technology, vol. 48, no. 5, pp. 1596-1609, 1999;    7) B. Yang, K. B. Letaief R. S. Cheng, and Z. Cao, “Timing recovery for OFDM transmission,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 11, pp. 2278-2291, 2000;    8) K. Takahashi and T. Saba, “A novel symbol synchronization algorithm with reduced influence of ISI for OFDM systems,” in Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '01), vol. 1, pp. 524-528, San Antonio, Tex., USA, November 2001;    9) P. Liu, B.-B. Li, Z.-Y. Lu, and F.-K. Gong, “A novel symbol synchronization scheme for OFDM,” in Proceedings of the International Conference on Communications, Circuits and Systems, vol. 1, pp. 247-251, Elong Kong, May 2005;    10) D. Lee and K. Cheun, “Coarse symbol synchronization algorithms for OFDM systems in multipath channels,” IEEE Communications Letters, vol. 6, no. 10, pp. 446-448, 2002;    11) A. Palin, J. Pikkarainen, and J. Rinne, “Improved symbol synchronization method in OFDM system in channels with large delay spreads,” in Proceedings of the 1st International Symposium on Communication Systems and Digital Signal Processing (CSDSP '98), pp. 309-312, Sheffield, UK, April 1998;    12) Y.-L Huang, C.-R. Sheu, and C.-C. Huang, “Joint synchronization in Eureka 147 DAB system based on abrupt phase change detection,” IEEE Journal on Selected Areas in Communications, vol. 17, no. 10, pp. 1770-1780, 1999;    13) A. Palin and J. Rinne, “Enhanced symbol synchronization method for OFDM system in SFN channels.” in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '98), vol. 5, pp. 2788-2793, Sydney Australia, November 1998;    14) S. H. Son and J. T. Kim, “A robust coarse symbol timing synchronization for OFDM systems in multi-path fading channel,” in Proceedings of the IEEE International Sympositum on Consumer Electronics 2008(ISCE 2008), pp. 1-3, Vilamoura, April 2008 (ISBN: 978-1-4244-2422-1); and    15) C. Williams, S. McLaughlin, and M. A. Beach, “Robust OFDM timing synchronisation in multipath channels,” EURASIP Journal on Wireless Communications and Networking, vol. 2008, Article ID 675048, 12 pages, 2008 (revised Feb. 19, 2008, accepted Apr. 21, 2008).
However, the ability of the methods proposed in the above-mentioned references for providing accurate timing and frequency estimation in a wide range of multipath channels is limited, as discussed below.
As mentioned above, timing synchronization is important in OFDM-based systems. For such timing synchronization, a timing window should be acquired at the receive side for an OFDM system to get the correct time domain sampling points for FFT operation. Thus, a time synchronization process is employed to acquire the time window for the FFT operation.
As mentioned above, various techniques are known in the art for performing the timing synchronization. Certain known systems utilize pilot-assisted synchronization methods based on a number of different pilot synchronization signals. For instance, one known technique for timing synchronization is preamble based. For example, in 802.11 there is a dedicated preamble, which may be referred to as a “training sequence,” that is used to perform the timing synchronization. Other systems do not use such a preamble for timing synchronization. So-called “blind” algorithms known in the art generally do not use any pilot training signals and typically exploit the correlation of the OFDM CP for timing synchronization. While blind methods are generally not wasteful of bandwidth on synchronization pilots, the synchronization accuracy is typically not as good as that attained using pilot-assisted methods. In certain continual transmission systems, such as the DVB-T, a dedicated preamble is not present, and so some embedded signals are used to perform the timing synchronization. For instance, such an embedded signal that may be used to perform the timing synchronization is the cyclic prefix (CP), which is the copy of the end of the OFDM signal boundary.
FIG. 1 shows an exemplary representation of a received OFDM symbol to illustrate the use of the embedded CP in a CP-correlation based method for performing the timing synchronization. Various mathematical variables are illustrated in FIG. 1, which are discussed further hereafter. As used herein, r(k) refers to the received OFDM signal that is received over time k; Ng refers to the length (in time) of CP; N refers to the length (in time) of the OFDM body; Ns refers to the full OFDM symbol (that includes both the CP and the OFDM body); and m* refers to the starting sampling point of a full OFDM symbol (generally once m* is known, the [m*+Ng: m*+Ng+N−1] can be used to perform FFT operation). Thus, the illustrated bar in FIG. 1, labeled r(k), represents the received OFDM symbol, which is shown with preceding dots and succeeding dots that represent other OFDM symbols that may be received over time.
As shown in FIG. 1, the CP represents the OFDM symbol boundary. In general, the CP of the OFDM symbol is exactly the same as the ending portion of the OFDM body. In the CP-correlation based timing synchronization technique, an algorithm is employed to perform a correlation between two windows. So, the system continues to receive a signal, and the correlation technique continues to perform the CP correlation. When the signal is received, it is buffered. Then, the CP-correlation technique performs correlation between the CP and the ending portion of the OFDM body, which generally reside at head of the buffer and the end of the buffer and are exactly one of the symbols apart. Because the CP and the ending portion of the OFDM body are the same, the correlation should ideally result in a peak power to be detected by a peak detector. Thus, the CP-correlation method is one technique for determining a timing window for sampling points for FFT operation.
FIG. 2 further illustrates an example of performing the traditional CP-correlation method. As illustrated, the CP correlation function, cor(m), performed on the received signal r(k) performs correlation between two Ng length sliding windows that are N delay apart. The output of the CP correlation function (cor(m)) performed on the received signal r(k) is shown as output 201 in FIG. 2. The output 201 of the correlation function has a substantially triangular shape in time domain with 2*Ng width. That is, over time 2*Ng, the power value of the correlation output signal 201 gradually increases until it peaks (at time point m*), and then gradually decreases, thereby forming the substantially triangular shape illustrated in FIG. 2 with the time axis forming the base of the triangle, the rising (or increasing) edge of the output signal 201 forming a second side of the triangle, and the falling (or decreasing) edge of the output signal 201 forming the third side of the triangle. As shown in FIG. 2, the correlation output 201 approaches its maximum (or peak) value at the OFDM symbol boundary due to the replica property between CP and the tail part of the OFDM body. As shown in FIG. 2, the peak value of correlation output 201 is repeated every OFDM symbol duration.
Generally speaking, there often exists more than one path received in an OFDM signal. That is, OFDM systems often have a multiple path transmission. So, multiple paths may be received, and in order to decode the OFDM signal correctly, it becomes desirable to detect the first-received path. Prior ranging processes have merely relied upon peak detection with respect to the received ranging signal. However, the peak often does not correspond to the first path (i.e., the first path is often not the strongest path). Establishing time delay based upon the ranging signal as received in other than the first path results in improper timing and may cause undesired signal characteristics such as inter-symbol interference (ISI). That is, if the timing is determined by the maximum triangular power signal detected and the first path is not the strongest path, part of the cyclic prefix of the next symbol will be included in the FFT window of the current symbol. Thus, ISI will be generated due to wrong timing. Accordingly, traditional ranging signal time delay determination based solely on peak value detection is less than optimal.
As illustrated in FIG. 3, multiple copies of signals may be received with different delay in the multipath propagation environment. For instance, signals 301-303 are illustrated as being received with different delay in the exemplary, multipath propagation environment of FIG. 3. FIG. 3 goes on to illustrate that it is generally desirable to perform the timing synchronization with the first path (as illustrated by timing synchronization 304) so as to avoid ISI. For instance, the exemplary timing synchronization 305 with the second path results in ISI caused by the first path in the illustrated example of FIG. 3. Therefore, FIG. 3 illustrates that it is generally desirable to acquire the first path in order to avoid ISI.
FIG. 4 illustrates an exemplary application of the traditional CP correlation technique when applied to a multipath propagation environment such as that of FIG. 3. The peak value detection can only detect the path with the largest power, rather than detecting the first path. When the traditional CP correlation function (as discussed above with FIG. 2) is applied to the received multipath signal 401 in FIG. 4, the correlation function output 402 produces a peak value 403 that does not correspond to the first path of the received signal 401. Multipath signal 401 is received, which in this example includes paths 410, 411, and 412. The first path 410 is received first in time, the second path 411 begins second in time, and the third path 412 begins third in time within the received multipath signal 401. As discussed further below, application of the traditional CP correlation function to the received multipath signal 401 in FIG. 4 results in detection of a peak value 403 that does not correspond to the first path 410 of the received signal 401.
The CP correlation function in the multipath environment is a superposition of multiple triangles that each corresponds to one path in the received signal 401. For instance, a first triangular correlation contribution 404 corresponds to the first path 410 in the received signal 401, wherein the first triangular contribution 404 has its peak value 407 coinciding with the boundary of the first path 410 in the received signal 401. A second triangular correlation contribution 405 corresponds to the second path 411 in the received signal 401, wherein the second triangular contribution 405 has its peak value 408 coinciding with the boundary of the second path 411 in the received signal 401. And, a third triangular correlation contribution 406 corresponds to the third path 412 in the received signal 401, wherein the third triangular contribution 406 has its peak value 409 coinciding with the boundary of the third path 412 in the received signal 401. The different triangular contributions 404, 405, and 406 all contribute to the correlation output 402. Generally the triangular contributions 404-406 are summed to produce the resulting correlation output 402 that is monitored by the peak detector. As such, the contributing triangular contributions 404-406 are effectively embedded within the resulting correlation output 402. While triangular contributions 404-406 are illustrated individually in FIG. 4, it should be understood that these contributions are generally not individually known (or detected) but are instead merely embedded as contributing components within correlation output 402. Thus, in the example illustrated in FIG. 4, the peak detector detects peak 403, which in this example coincides with the boundary of the second path 411, rather than the first path 410.
Accordingly, a problem becomes how to accurately detect the first-received path (e.g., path 410) in a multipath environment. In other words, it becomes desirable to detect the peak value 407 of the triangular contribution 404 that corresponds to the first path 410.
In view of the above, the traditional CP correlation method for OFDM timing synchronization is not robust in a multipath environment when the strongest multipath components are delayed relative to the first arriving paths. One technique that has been proposed for attempting to detect the first-received path is illustrated with FIGS. 5A-5D. See e.g., C. Williams, S. McLaughlin, and M. A. Beach, “Robust OFDM timing synchronisation in multipath channels,” EURASIP Journal on Wireless Communications and Networking, vol. 2008, Article ID 675048, 12 pages, 2008 (revised Feb. 19, 2008, accepted Apr. 21, 2008). The technique illustrated in FIGS. 5A-5D is referred to herein as the “largest slope” detection method.
This largest slope detection method operates on the principle that the slope of the correlation curve increases before the first path and starts to decrease after the first path. Thus, the end of the segment of the correlation curve with the largest slope is detected as coinciding with the peak of the first path, as illustrated in FIGS. 5A and 5B. For instance, FIG. 5A shows an example in which there are two correlation “triangular” contributions 501 and 502 that correspond, respectively, to a first-received path and second-received path that are included in a received signal (such as paths 410 and 411 in the example of FIG. 4 discussed above). FIG. 5A shows an example in which the power of the peak 505 of the correlation “triangular” contribution 501 for the first path is greater than the peak of the correlation “triangular” contribution 502 for the second path. The resulting CP correlation output has a curve having a segment 503A with a first slope and a segment 503B with a different slope. The slope of the first segment 503A increases, and then at point 504 the slope starts decreasing for segment 503B. As can be seen in FIG. 5A, the point 504 at which the slope of the CP correlation output curve begins decreasing corresponds to the peak 505 of the correlation “triangular” contribution 501 for the first path. Thus, by employing the largest slope detection method to detect point 504, the peak 505 of the correlation “triangular” contribution 501 for the first path in a received signal may be detected.
FIG. 5B shows another example in which there are two correlation “triangular” contributions 521 and 522 that correspond, respectively, to a first path and second path that are included in a received signal (such as paths 410 and 411 in the example of FIG. 4 discussed above). FIG. 5B shows an example in which the power of the peak 525 of the correlation “triangular” contribution 521 for the first path is less than the peak of the correlation “triangular” contribution 522 for the second path. The resulting CP correlation output has a curve having a segment 523A with a first slope and a segment 523B with a different slope. The slope of the first segment 523A increases, and then at point 524 the slope is decreased for segment 523B. As can be seen in FIG. 5B, the point 524 at which the slope of the CP correlation output curve decreases corresponds to the peak 525 of the correlation “triangular” contribution 521 for the first path. Thus, by employing the largest slope detection method to detect point 524, the peak 525 of the correlation “triangular” contribution 521 for the first path in a received signal may be detected.
However, the determination of the largest slope is extremely difficult due to the noisy feature of the practical correlation curve. For instance, FIG. 5C illustrates an example of a CP correlation curve 530 that may be produced in practical application in a real-world system. As shown in the enlarged portion 530A in the example of FIG. 5C, the largest slope method may lead to a false detection of the first path at an erroneous point 531 due to noise that is present in the system. That is, due to noise, the largest slope observed in the CP correlation output may not coincide with the peak of the first triangular output for the first path. Particularly if the time window over which the correlation slope is being evaluated is quite small, then the noise may greatly affect the determination of the slope. So, FIG. 5C illustrates that if the gradient of the correlation curve 530 is determined at very small windows, then the largest slope is possibly detected at some random point, such as point 531 shown in FIG. 5C. Because of this sensitivity to noise the largest slope method requires use of a lot of filtering technologies. As a result, the largest slope method is undesirably difficult to implement and/or its results are not as dependable as may be desired. For instance, FIG. 5D shows a block diagram of the complicated structure 540 that is used for performing the largest slope synchronization method, as described further in C. Williams et al. “Robust OFDM timing synchronisation in multipath channels” cited above.